A Modified Generalized Analytic Feynman Integral Associated with the Bounded Linear Operator

Abstract

In this paper, we define a modified and generalized analytic Feynman integral associated with the bounded linear operator on abstract Wiener spaces. We then prove its existence. We also establish some modified and generalized analytic Feynman integration formulas and relationships involving the generalized Cameron–Storvick theorem. Finally, we give some examples to explain the usefulness of our research.

Keywords

• generalized analytic Feynman integral
• bounded operator
• translation theorem
• first variation
• Cameron–Storvick theorem
• abstract Wiener space